Goursat problem in hyperbolic partial differential equations with variable coefficients solved by Taylor collocation method

Document Type : Research Article

Authors

• Fouzia Birem
• Aissa Boulmerka
• Hafida Laib
• Chahinaz Hennous

Laboratory of Mathematics and their interactions, University Center Abdelhafid Boussouf, Mila, Algeria

10.22067/ijnao.2024.85895.1364

Abstract

The Hyperbolic Partial Differential Equation (PDE) has important practical uses in science and engineering. This article provides an estimate for solving the Goursat Problem in Hyperbolic Linear PDEs with variable coefficients. The Goursat PDE is transformed into a second kind of linear Volterra Integral Equation (VIE). A convergent algorithm that employs Taylor polynomials is created to generate a collocation solution and the error using the maximum norm is estimated. The paper includes numerical examples to prove the method's effectiveness and precision.

Keywords

• Hyperbolic partial differential equations
• Goursat problem
• Volterra integral equation
• Collocation method
• Taylor polynomials

Main Subjects

• Numerical methods for integral equations and its applications

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